A new method to solve the neutron transport problem of spherical structure

The Boltzmann equation is an integro-differential equation representing a wide range of transport and radiative transfer problems. In this paper, we propose to use the half boundary method (HBM) in the spherical coordinate system for deriving accurate and robust numerical solutions of the Boltzmann transport equation for neutron transport problem, respectively for vacuum boundary conditions, reflection boundary conditions and multilayer dielectric materials, yielding the recursive equation of the angular neutron flux by discretizing the transport equation's space and angle variables. The relationship between any point and the boundary point is derived and the particle flux distribution is obtained. Compared to traditional discrete ordinate method, the HBM uses no inverse matrix, which increases the degree of discretion, significantly reducing the computation expenses in the solution process. Finally, the HBM results are compared to those of the Monte Carlo method, proving the proposed method's feasibility, high accuracy and applicability.